So there’s this video that posits only four colors are necessary for a map. The key issue is that it assumes that countries and states must be contiguous. This isn’t true. For an easy example, look at the U.S.A. Alaska is all alone up northwest of Canada. The theory is that there is no configuration that can create a map requiring more than 4 colors. This is simply incorrect! I made a very crude drawing showing why.
As you can see, Swarzia is split into two geographical locations, split by Nolor. If Northwest Swarzia were another country, this could work with four colors. Shifton could be Red just like Swarzia and NE Swarzia could be yellow, letting Melitus be blue instead.
The theory only works when you consider a “country” a contiguous landmass. We know this isn’t true, especially among allied nations. In fact, look at the Navajo/Hopi nations in Arizona.
I know, I used a GGP Grey video despite the guy having serious misunderstandings about the electoral college system and why it’s necessary for preserving the American ideal of protecting the minority from the majority.
Ultimately, it’s possible to have a map that actually requires more than four colors. The problem isn’t in Numberphile’s math. It’s in the application of that math with specific constrictions that don’t apply to real-world politics or borders. I get the proof, but I disagree that it applies to real situations. Not everything is a perfect sphere with 9.8 m/s/s applied to it. The problem is that in my example, crude as it may be, Melitus is capable of touching four different other nations, some of which also touch each-other.
It’s an artistic proof, but it’s realistic. Alaska is evidence enough that maps may, with the right borders, require more than four colors. Now imagine if Shifton took a column of Borgar, but left part of Borgar as part of its parent country, and Borgar squeezed out a corridor of Swazia that neighbored Melitus. It gets worse. Much worse.